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Simplifying 7x2 + 19x = 10000 Reorder the terms: 19x + 7x2 = 10000 Solving 19x + 7x2 = 10000 Solving for variable 'x'. Reorder the terms: -10000 + 19x + 7x2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 -10000 + 19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1428.571429 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '1428.571429' to each side of the equation. -1428.571429 + 2.714285714x + 1428.571429 + x2 = 0 + 1428.571429 Reorder the terms: -1428.571429 + 1428.571429 + 2.714285714x + x2 = 0 + 1428.571429 Combine like terms: -1428.571429 + 1428.571429 = 0.000000 0.000000 + 2.714285714x + x2 = 0 + 1428.571429 2.714285714x + x2 = 0 + 1428.571429 Combine like terms: 0 + 1428.571429 = 1428.571429 2.714285714x + x2 = 1428.571429 The x term is 2.714285714x. Take half its coefficient (1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. 2.714285714x + 1.841836734 + x2 = 1428.571429 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 1428.571429 + 1.841836734 Combine like terms: 1428.571429 + 1.841836734 = 1430.413265734 1.841836734 + 2.714285714x + x2 = 1430.413265734 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 1430.413265734 Calculate the square root of the right side: 37.820804668 Break this problem into two subproblems by setting (x + 1.357142857) equal to 37.820804668 and -37.820804668.Subproblem 1
x + 1.357142857 = 37.820804668 Simplifying x + 1.357142857 = 37.820804668 Reorder the terms: 1.357142857 + x = 37.820804668 Solving 1.357142857 + x = 37.820804668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + x = 37.820804668 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 37.820804668 + -1.357142857 x = 37.820804668 + -1.357142857 Combine like terms: 37.820804668 + -1.357142857 = 36.463661811 x = 36.463661811 Simplifying x = 36.463661811Subproblem 2
x + 1.357142857 = -37.820804668 Simplifying x + 1.357142857 = -37.820804668 Reorder the terms: 1.357142857 + x = -37.820804668 Solving 1.357142857 + x = -37.820804668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + x = -37.820804668 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -37.820804668 + -1.357142857 x = -37.820804668 + -1.357142857 Combine like terms: -37.820804668 + -1.357142857 = -39.177947525 x = -39.177947525 Simplifying x = -39.177947525Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.463661811, -39.177947525}
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